The weak Lie 2-algebra of multiplicative forms on a quasi-Poisson groupoid

Quasi-Poisson groupoids are $(+1)$-shifted Poisson objects in the category of differentiable stacks. It is known that the space of multiplicative multivector fields on a Lie groupoid is a ($\mathbb{Z}$-)graded Lie $2$-algebra. In this paper we find a natural ($\mathbb{Z}$-)graded weak Lie $2$-algebra structure which is primarily composed of multiplicative forms on a quasi-Poisson groupoid. Moreover, a morphism between the two Lie $2$-algebras is established.